Abstract
In this paper we present explicit and simple analytical formulae for the energy eigenvaluesE n (λ) of one-dimensional anharmonic oscillators characterized by the potentials 1/2mω 2 x 2+λx 2α withα=2, 3 and 4. A simple intuitive criterion supplemented by the requirement of correct asymptotic behaviour, has been employed in arriving at the formulae. Our energy values over a wide range ofn andλ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge this is the first time that formulae of such wide validity have been given. The results for pure power oscillators are trivially obtained by going over to theω→0 limit. Approximate analytic expressions for the low order even moments ofx are also given.
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Mathews, P.M., Seetharaman, M., Raghavan, S. et al. On the energy spectra of one-dimensional anharmonic oscillators. Pramana - J Phys 17, 121–134 (1981). https://doi.org/10.1007/BF02875428
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DOI: https://doi.org/10.1007/BF02875428